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Theorem mtordOLD 26218
Description: A modus tollens deduction involving disjunction. (Moved into main set.mm as mtord 641 and may be deleted by mathbox owner, JGH. --NM 29-May-2014.) (Contributed by Jeff Hankins, 15-Jul-2009.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
mtordOLD.1  |-  ( ph  ->  -.  ch )
mtordOLD.2  |-  ( ph  ->  -.  th )
mtordOLD.3  |-  ( ph  ->  ( ps  ->  ( ch  \/  th ) ) )
Assertion
Ref Expression
mtordOLD  |-  ( ph  ->  -.  ps )

Proof of Theorem mtordOLD
StepHypRef Expression
1 mtordOLD.1 . 2  |-  ( ph  ->  -.  ch )
2 mtordOLD.2 . 2  |-  ( ph  ->  -.  th )
3 mtordOLD.3 . 2  |-  ( ph  ->  ( ps  ->  ( ch  \/  th ) ) )
41, 2, 3mtord 641 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359
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